New models for econometric analysis of dynamic event histories: with application to British fertility data

This article considers an econometric modeling problem of a recurrent discrete binary-valued outcome observed at irregular intervals, e.g. birth, emergency room visit, hospital admission. Both the number of and the duration between events vary across units. Over a period of time discrete process generates a dynamic event history if recurrent events show lagged dependence or initial value dependence. Complex dynamic dependence as well as the irregular data structure pose a modeling challenge.

The paper considers three classes of dynamic models: 1. Modified dynamic event history (MDEH) model; 2. Dynamic panel logit (DPL) model; 3. Generalized autocorrelation conditional duration (GACD) model.   Past theoretical and empirical work emphasizes the dependence of a new birth outcome on previous history outcomes. Dynamics also have a key role in distinguishing between the effect of individual time-invariant unobserved heterogeneity and pure state dependence.

The MDEH and DPL models are specified in terms of conditional hazard of birth, conditioning on economic and socio-demographic factors, on individual and parity-specific fixed or random effects, and the event history. The GACD model, whose previous applications are mainly in empirical finance, analyzes the elapsed duration between successive births while controlling for lagged dependence and relevant covariates. All models capture dependence on previous outcomes, albeit in different ways. All three model classes are of the reduced form variety; however, the MDEH model has points of contact with structural models of fertility in which agents optimally choose both the number of children and the spacing of births.

We use retrospective fertility data, complemented with longitudinal data, from the British Household Panel Survey (BHPS), a longitudinal study that began in 1991 and ended in 2008.  The BHPS is one of the best suited existing surveys to analyze fertility histories in a developed country with a well-established fertility transition. The sample contains information for 16,404 women aged 15 and over and followed annually during the 1992-2008 period.  This provides a hierarchical and longitudinal data structure, with newly reported children nested within years, years nested within parity, and parity nested within individuals. Therefore, it is possible to build a detailed and complete fertility history for all adult women in the sample, a feature that allows us to model the current probability of a birth as a function of qualitative features of past outcomes, the outcomes themselves, and economic and socio-demographic factors.  A key contribution is the paper’s proposed method of recasting event history data into a more panel-data like format which can then exploit panel data methods, especially those for controlling individual and parity-specific unobserved heterogeneity. Conditional maximum likelihood is used in estimating the models.  

We compare the relative performance, key results and implications of models. There is robust evidence for parity fixed effects, initial condition effect, gender balance preference, mother’s education and family-level socio-economic variables. Evidence indicates a role for state dependence even after controlling for other lagged variables.  Both MDEH and DPL outperform the GACD model; however, overall, the MDEH model appears to be the best.